Distancesum heterogeneity in graphs and complex networks
Estrada, Ernesto and Vargas Estrada, Eusebio (2012) Distancesum heterogeneity in graphs and complex networks. Applied Mathematics and Computation, 218 (21). pp. 1039310405. ISSN 00963003 (https://doi.org/10.1016/j.amc.2012.03.091)
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The heterogeneity of the sum of all distances from one node to the rest of nodes in a graph (distancesum or status of the node) is analyzed. We start here by analyzing the cumulative statistical distributions of the distancesum of nodes in random and realworld networks. From this analysis we conclude that statistical distributions do not reveal the distancesumheterogeneity in networks. Thus, we motivate an index of distancesumheterogeneity based on a hypothetical consensus model in which the nodes of the network try to reach an agreement on their distancesum values. This index is expressed as a quadratic form of the combinatorial Laplacian matrix of the network. The distancesumheterogeneity index φ(G) gives a natural interpretation of the Balaban index for any kind of graph/network. We conjecture here that among graphs with a given number of nodes φ(G) is maximized for a graph with a structure resembling the agave plant. We also found the graphs that maximize φ(G) for a given number of nodes and links. Using this index and a normalized version of it we studied random graphs as well as 57 realworld networks. Our findings indicate that the distancesumheterogeneity index reveals important structural characteristics of networks which can be important for understanding the functional and dynamical processes in complex systems.
ORCID iDs
Estrada, Ernesto ORCID: https://orcid.org/0000000230667418 and Vargas Estrada, Eusebio;

Item type: Article ID code: 40673 Dates: DateEvent1 July 2012PublishedKeywords: distance distributions, distancesum, complex networks, Balaban index, graph distances, Mathematics, Computational Mathematics, Applied Mathematics Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 02 Aug 2012 12:52 Last modified: 29 Sep 2022 01:33 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/40673